Difference between revisions of "Adjoint surface"
From Encyclopedia of Mathematics
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A surface $Y$ that is in [[Peterson correspondence|Peterson correspondence]] with a given surface $X$ and is, moreover, such that the asymptotic net on $Y$ corresponds to a conjugate net $\sigma$ on $X$ with equal invariants, and vice versa. The adjoint surface $Y$ is the [[Rotation indicatrix|rotation indicatrix]] for $X$, and vice versa. If $\sigma$ is a principal base for a deformation of $X$, then $Y$ is a [[Bianchi surface|Bianchi surface]]. | A surface $Y$ that is in [[Peterson correspondence|Peterson correspondence]] with a given surface $X$ and is, moreover, such that the asymptotic net on $Y$ corresponds to a conjugate net $\sigma$ on $X$ with equal invariants, and vice versa. The adjoint surface $Y$ is the [[Rotation indicatrix|rotation indicatrix]] for $X$, and vice versa. If $\sigma$ is a principal base for a deformation of $X$, then $Y$ is a [[Bianchi surface|Bianchi surface]]. | ||
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Revision as of 12:40, 2 November 2014
A surface $Y$ that is in Peterson correspondence with a given surface $X$ and is, moreover, such that the asymptotic net on $Y$ corresponds to a conjugate net $\sigma$ on $X$ with equal invariants, and vice versa. The adjoint surface $Y$ is the rotation indicatrix for $X$, and vice versa. If $\sigma$ is a principal base for a deformation of $X$, then $Y$ is a Bianchi surface.
How to Cite This Entry:
Adjoint surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_surface&oldid=31986
Adjoint surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjoint_surface&oldid=31986
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article